Feynman diagram
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Imagine you wanted to bookkeep all the ways two billiard balls could glance off each other, but the balls are subatomic particles that can also emit, absorb, and briefly turn into other particles. You need a clear way to draw each possible story of what happened. A Feynman diagram is exactly that: a simple cartoon, invented by the physicist Richard Feynman in the late 1940s, where lines represent particles moving and points where lines meet represent interactions. Time usually runs in one direction across the page, so you can read a diagram almost like a comic strip of a collision.
Crucially, a Feynman diagram is not a literal photograph of paths through space. It is a precise piece of mathematical shorthand. Each part of the picture stands for a specific factor in a calculation: every line and every meeting point corresponds to a number you multiply together, and the whole diagram evaluates to a contribution to the amplitude for the process. So a physicist draws all the diagrams that lead from a starting set of particles to a finishing set, writes down the matching mathematical expression for each, adds them up, and squares the total to get a probability. The drawing and the equation are two faces of the same thing.
Feynman diagrams transformed particle physics because they made fearsomely complicated calculations organized and even intuitive. They are the everyday working language used to predict scattering rates, decay rates, and the tiny quantum corrections that have been confirmed to astonishing precision. A common misconception is to read the wiggly internal lines as real particles really travelling; the internal lines stand for virtual particles, which are a calculational device, not little objects you could ever catch in a detector.
The simplest diagram for two electrons repelling shows two incoming electron lines, one outgoing line from each, and a single wavy photon line passing between them. Reading it: the electrons exchange a photon, and that exchange is electromagnetic repulsion. That one little picture is the whole leading-order story of how like charges push apart.
Two electrons swap a photon — repulsion, drawn.
A Feynman diagram is a mnemonic for a term in a calculation, not a literal trajectory; the internal lines are virtual particles, not objects you could observe directly.